machining chip-breaking prediction with grooved inserts in ......grooved cutting tools, and a...

Machining Chip-Breaking Prediction

with Grooved Inserts in Steel Turning by

Li Zhou

A Ph.D. Research Proposal

Submitted to the faculty of the

WORCESTER POLYTECHNIC INSTITUTE

in partial fulfillment of the requirements for the

Degree of Doctor of Philosophy

in

Manufacturing Engineering

by

December 2001

Committee members:

______________________________________________ Professor Yiming Rong, Major Advisor

______________________________________________ Professor Christopher A. Brown, MFE Program Director

Professor Richard D. Sisson, Member

Professor Mustapha S. Fofana, Member

Professor Ning Fang, Member

ii

Abstract

Prediction of chip-breaking in machining is an important task for automated

manufacturing. There are chip-breaking limits in maching chip-breaking processes, which

determine the chip-breaking range. This paper presents a study of chip-breaking limits with

grooved cutting tools, and a web-based machining chip-breaking prediction system. Based

on the chip-breaking curve, the critical feed rate is modeled through an analysis of up-curl

chip formation, and the critical depth of cut is formulated through a discussion of side-curl

dominant chip-formation processes. Factors affecting chip-breaking limits are also

discussed.

In order to predict chip-breaking limits, semi-empirical models are established.

Although the coefficients that occur in the model are estimated through machining tests,

the models are applicable to a broad range of machining conditions. The model parameters

include machining conditions, tool geometry, and workpiece material properties. A new

web-based machining chip-breaking prediction system is introduced with examples of

industrial applications.

iii

Acknowledgments

Throughout the course of this project, I have interacted with many people who have

influenced the development of my professional work as well as my personal growth. I

would like to thank the following people:

My advisor, Professor Yiming Rong, for his guidance and support throughout my

years at WPI. His patience and expertise helped me find direction in many endeavors. I

have very much enjoyed and benefited from the intellectual discussions that we had during

this time. Without his mentoring and encouragement this work could not have been done.

My other committee members, Professor Christopher Brown, Professor Richard

Sisson, and Professor Mustafa Fofana, for their enthusiastic service on the thesis

committee. Their useful comments has been very helpful in improving my writing style.

Dr. Ning Fang and Dr. Juhchin Yang, for providing me a precious opportunity to

apply my research into industry and for guiding me in the machining chip-control area

from the very beginning. The research grant assistantship provided by Ford Powertrain is

also acknowledged.

Professor Zhengjia Li, from Harbin University of Science & Technology, Harbin,

China, for guiding me in the research work.

Dr. Mingli Zheng, Mr. Hong Guo, and Mr. Richard John Cournoyer, for assisting

me in my experimental work.

The members of the CAM Lab at WPI. All of them provided companionship and

kept work fun in addition to providing valuable scholarly input.

Finally, I would like to dedicate this thesis to my wife, my parents, and my

brother for their constant love, support, education, and patience during my studies.

iv

Nomenclature

f Feed rate

d Depth of cut

V Cutting speed

fcr The critical feed rate

dcr The critical depth of cut

f0 The standard critical feed rate under pre-defined standard cutting condition

d0 The standard critical depth of cut under pre-defined standard cutting condition

Ch Cutting ratio (the ratio of the undeformed chip thickness and the chip thickness) ψλ Chip flow angle

hch Chip thickness

αhch Distance from neutral axial plane of the chip to the chip surface

rε Insert Nose radius

Wn Insert chip-breaking groove width

κγ Cutting edge angle

γ0 Insert rake angle

γn Insert rake angle in normal direction

γ01 Insert land rake angle

λs Insert inclination angle

bγ1 Insert/chip restricted contact length

h Insert backwall height

δ Chip scroll angle in side-curl

εB Chip-breaking strain (workpiece fracture strain)

θ Chip flow angle

η Chip back flow angle

v

fmK Modification coefficient of the workpiece material effect on the critical

feed rate

fVK Modification coefficient of the cutting speed effect on the critical

feed rate

fTK Modification coefficient of the cutting tool (insert) effect on the critical

feed rate

εfrK Modification coefficient of the cutting tool (insert) nose radius effect on

the critical feed rate

fWnK Modification coefficient of the cutting tool (insert) chip-breaking groove

width effect on the critical feed rate

rfkK Modification coefficient of the cutting edge angle effect on the critical

feed rate

0γfK Modification coefficient of the cutting tool (insert) rake angle effect on


1rfbK Modification coefficient of the cutting tool (insert) land length effect on


01γfK Modification coefficient of the cutting tool (insert) land rake angle effect

on the critical feed rate

fhK Modification coefficient of the cutting tool (insert) backwall height effect

on the critical feed rate

dmK Modification coefficient of the workpiece material effect on the critical

depth of cut

dVK Modification coefficient of the cutting speed effect on the critical

depth of cut

dTK Modification coefficient of the cutting tool (insert) effect on the critical

depth of cut

εdrK Modification coefficient of the cutting tool (insert) nose radius effect on

vi

the critical depth of cut

dWnK Modification coefficient of the cutting tool (insert) chip-breaking groove width effect on the critical depth of cut

rdkK Modification coefficient of the cutting edge angle effect on the critical

depth of cut

0γdK Modification coefficient of the cutting tool (insert) rake angle effect on


1rdbK Modification coefficient of the cutting tool (insert) land length effect on


01γdK Modification coefficient of the cutting tool (insert) land rake angle effect

on the critical depth of cut

dhK Modification coefficient of the cutting tool (insert) backwall height effect

on the critical depth of cut

RK Coefficient related to the chip radius breaking

lc Chip / tool contact length

M Bending moment

PT Chip gravity force

PW Friction force between chip and workpiece

RC Chip up-curl radius

ρ Chip side-curl radius

RL Chip-breaking radius

i

Table of Contents

Abstract ii

Acknowledgments.................................................................................................. iii

Nomenclature ......................................................................................................... iv

List of Figures ........................................................................................................ iv

List of Tables......................................................................................................... vii

1 Introduction .............................................................................................. 1

1.1 Overview of Machining Chip Formation............................................ 1

1.2 Chip-Breaking Groove & Cutting Tool Classification ....................... 7

1.3 Chip-Breaking Limits ......................................................................... 9

2 The State of the Art ................................................................................ 12

2.1 Chip Flow.......................................................................................... 12

2.2 Chip Curl........................................................................................... 15

2.2.1. Chip Up-Curl ................................................................................ 15

2.2.2. Chip Side-Curl .............................................................................. 17

2.2.3. Chip Lateral-Curl and Combination Chip Curl ............................ 18

2.3 Chip-Breaking................................................................................... 19

2.4 Nakayama's Chip-Breaking Criterion............................................... 21

2.5 Li’s Work on Chip-Breaking ............................................................ 22

2.5.1. Theoretical Analysis of fcr and dcr................................................. 22

2.5.2. Semi-Empirical Chip-Breaking Predictive Model........................ 25

2.6 Existing Problems ............................................................................. 29

3 Objectives and Scope of Work ............................................................... 31

3.1 Approach........................................................................................... 31

3.2 Objectives ......................................................................................... 32

3.3 Outline of the Dissertation ................................................................ 33

4 Extended Study on Chip-Breaking Limits for

Two-Dimensional Grooved Inserts......................................................... 35

4.1 Geometry of Two-Dimensional Grooved Inserts ............................. 35

4.2 The Critical Feed Rate (fcr) ............................................................... 36

ii

4.2.1. Equation of the Chip Up-curl Radius RC ...................................... 36

4.2.2. Equation of the Critical Feed Rate fcr ........................................... 39

4.3 The Critical Depth of Cut ................................................................. 39

4.4 Semi-Empirical Chip-Breaking Model for

Two-Dimensional-Grooved Inserts ................................................. 43

4.5 Experimental Work........................................................................... 44

4.5.1. Design of the Experiments............................................................ 45

4.5.2. Experimental Results .................................................................... 46

4.5.3. Experimental Data Analysis ......................................................... 47

4.5.3.1. Rake Angle................................................................................. 48

4.5.3.2. Land Length ............................................................................... 48

4.5.3.3. Land Rake Angle ....................................................................... 49

4.5.3.4. Raised Backwall Height............................................................. 49

4.6 Summary ........................................................................................... 54

5 Chip-Breaking Predictive Model for

Three-Dimensional Grooved Inserts ...................................................... 56

5.1 Definition of Three-dimensional Grooved Inserts............................ 56

5.2 Insert feature parameters................................................................... 58

5.3 Feature Parameters Based Predictive Model

of Chip-Breaking Limits .................................................................. 60

5.4 Semi-empirical Chip-Breaking Prediction Model ............................ 63

5.5 Design of the Experiments................................................................ 64

5.6 Experimental Results ........................................................................ 69

5.7 Experiment-based Predictive Model of Chip-Breaking Limits ........ 80

5.8 Summary ........................................................................................... 83

6 Web-Based Machining Chip-Breaking Predictive System..................... 85

6.1 Introduction of the System................................................................ 85

6.2 System Structure ............................................................................... 87

6.3 Chip Shape / Length Prediction ........................................................ 88

6.3.1. Chip Classification........................................................................ 88

6.3.2. Chip-Breaking Chart and Chip-Breaking Matrix ......................... 89

iii

6.4 System Databases.............................................................................. 91

6.4.1. Insert Database.............................................................................. 92

6.4.2. Work-Piece Material Database...................................................... 92

6.4.3. Using the Two Databases.............................................................. 92

6.5 Updating / Extending the System ..................................................... 93

6.5.1. Update / extend the insert Database.............................................. 93

6.5.2. Update / Extend the Work-Piece Material Database..................... 94

6.6 Web-Based Client-server Programming Technology....................... 95

6.6.1. Client-Server Technology ............................................................. 96

6.7 Introduction of the User Interface..................................................... 98

6.7.1. System Input ................................................................................. 99

6.7.2. System Output............................................................................. 103

6.8 Summary ......................................................................................... 104

7 Conclusions And Future Work ............................................................. 106

7.1 Summary of this Research .............................................................. 106

7.2 Future Work .................................................................................... 107

7.2.1. Inserts with Block-type Chip Breaker......................................... 108

7.2.2. Inserts with Complicated Geometric Modifications ....................111

Bibliography ........................................................................................................113

Appendix A. Sample Chip-breaking Charts of

Two-Dimensional Grooved Inserts....................................................... 122

Appendix B. Sample Chip-breaking Charts of

Three-dimensional Grooved Inserts ..................................................... 131

iv

List of Figures

Figure 1-1 Chip Flow........................................................................................................ 3

Figure 1-2 Chip Side-curl and Chip Up-curl (Jawahir 1993) ........................................... 4

Figure 1-3 Research Fields of Chip-Control..................................................................... 5

Figure 1-4 Classification of Chip Breaker / Chip-Breaking Groove ................................ 8

Figure 1-5 A Sample Chip-Breaking Chart ...................................................................... 9

Figure 1-6 Typical Chip-Breaking Chart (Li, Z. 1990) .................................................. 10

Figure 2-1 Chip Flow Angle (Jawahir, 1993)................................................................. 13

Figure 2-2 Chip Up-Curl Process with Grooved Cutting Tool (Li, Z. 1990) ................. 16

Figure 2-3 Mechanism of Chip Side-Curl ...................................................................... 18

Figure 2-4 Chip Flow of Side-Curl Dominated ε-Type Chips (Li, Z. 1990).................. 24

Figure 2-5 A Segment of ε-Type Chip and Its Cross Section (Li, Z. 1990) ................... 25

Figure 2-6 Factors Influence Chip Breakability ............................................................. 26

Figure 4-1 Geometry of Two-Dimensional Grooved Inserts.......................................... 35

Figure 4-2 The Geometric Parameters of Two-Dimensional Grooved Insert (1)........... 37

Figure 4-3 The Geometric Parameters of Two-Dimensional Grooved Insert (2)........... 38

Figure 4-4 A Segment of a ε-Type Chip and Its Cross Section (Li, Z. 1990) ............. 41

Figure 4-5 Depth of Cut and Cutting Flow Angle (Li, Z. 1990) .................................... 42

Figure 4-6 Rake Angle and Chip-Breaking Limits......................................................... 50

Figure 4-7 Land Length and Chip-Breaking Limits ....................................................... 51

Figure 4-8 Land Rake Angle and Chip-Breaking Limits................................................ 52

Figure 4-9 Raised Backwall Height and Chip-Breaking Limits..................................... 53

Figure 5-1 Three-Dimensional Grooved Insert............................................................... 57

Figure 5-2 Two Examples of Commercial Three-Dimensional Grooved Insert ............ 57

Figure 5-3 The Three-Dimensional Grooved Insert Geometric Features....................... 59

Figure 5-4 α and the Groove Width (Change α, Fix L) .................................................. 61

Figure 5-5 L and the Groove Width (Change L, Fix α) .................................................. 62

Figure 5-6 Geometry of a Special Kind of Industry Insert ............................................. 66

Figure 5-7 Screenshot of the Insert Geometry Measurement Software.......................... 67

Figure 5-8 Modeling Process for Three-Dimensional Grooved Inserts.......................... 68

v

Figure 5-9 Insert TNMP33xK-KC850............................................................................ 73

Figure 5-10 dcr VS εr for Different Insert Families ..................................................... 74

Figure 5-11 fcr VS εr for Different Insert Families ...................................................... 75

Figure 5-12 dcr: Experimental Results VS Model Predictive Results............................. 78

Figure 5-13 fcr: Experimental Results VS Model Predictive Results ............................. 79

Figure 6-1 System Flow Chart........................................................................................ 88

Figure 6-2 A Samples Chip-Breaking Chart................................................................... 90

Figure 6-3 Adding a New Cutting Tools to the System.................................................. 94

Figure 6-4 Adding a New Cutting Tools to the System.................................................. 95

Figure 6-5 Web-System Infrastructure ........................................................................... 98

Figure 6-6 User Interface of the System......................................................................... 99

Figure 6-7 Work-Piece Material Menu......................................................................... 100

Figure 6-8 Insert Menu ................................................................................................. 100

Figure 6-9 Nose Radius Menu ...................................................................................... 100

Figure 6-10 Cutting Condition Input ............................................................................ 101

Figure 6-11 Warning Message When Input Is Not in Range........................................ 101

Figure 6-12 Unit Selection............................................................................................ 102

Figure 6-13 Help Information for User Input ............................................................... 102

Figure 6-14 Insert Geometry Diagram Shown in the System....................................... 103

Figure 6-15 Screen Shot of the System Output and Help Window .............................. 105

Figure 7-1 Illustration of the Geometry of the Block-Type Chip Breaker ................... 109

Figure 7-2 Modeling Process for Inserts with Block-Type Chip Breaker .................... 110

Figure 7-3 A Sample Chip-Breaking Chart of Copper Cutting

with Inserts having Block-Type Chip-Breaker ........................................... 111

Figure 7-4 A Sample Chip-Breaking Chart with Inserts

with Complicated Geometric Modifications............................................... 112

Figure A-1 The Chip-Breaking Chart Got from Insert 1 .............................................. 122




Figure A-5 The Chip-Breaking Chart Got from Insert 10 ............................................ 126

vi





Figure B-1 Sample Chip-Breaking Chart; Insert: TNMG 331 QF4025 ....................... 132

Figure B-2 Sample Chip-Breaking Chart; Insert: TNMG 332 QF 4025 ...................... 133

Figure B-3 Sample Chip-Breaking Chart; Insert: TNMG 333 QF 4025 ...................... 134

Figure B-4 Sample Chip-Breaking Chart; Insert: TNMP 331K KC850....................... 135



Figure B-7 Sample Chip-Breaking Chart: TNMG 432 KC850 .................................... 138

Figure B-8 Sample Chip-Breaking Chart; Insert: TNMG 332-23 4035 ....................... 139

Figure B-9 Sample Chip-Breaking Chart; Insert: TNMG 332 4025 ............................ 140

Figure B-10 Sample Chip-Breaking Chart; Insert: TNMG 332MF 235....................... 141

vii

List of Tables

Table 4-1 Insert Geometric Parameters Design .............................................................. 45

Table 4-2 Cutting Test Results ....................................................................................... 46

Table 5-1 Insert Measurement Results ........................................................................... 70

Table 5-2 Cutting Test Results* ...................................................................................... 71

Table 5-3 KfT and KdT Results from Cutting Tests .......................................................... 82

Table 6-1 Chip Classification Used in the System ......................................................... 89

1

1 Introduction This chapter gives an overview of the chip-control in machining, followed by a

description of the chip-breaking groove / cutting tool classification.

1.1 Overview of Machining Chip Formation

Manufacturing processes can be classified into three categories, material joining,

forming, and removal processes (Trent, 2000). Machining process is a material removal

process. Conventionally, the concept of machining is described as removing metal by

mechanically forcing a cutting edge through a workpiece. It includes processes such as

turning, milling, boring, drilling, facing, and broaching, which are all chip-forming

operations. In the last few decades, some entirely new machining processes have been

developed, such as the ultrasonic machining, thermal metal removal processes,

electrochemical material removal processes, laser machining processes etc., which are

very different from the conventional machining processes. However, the conventional

metal cutting operations are still the most widely used fabrication processes, a $60billion

/per year business. It is still essential to develop a more fundamental understanding of

metal cutting processes.

Although conventional metal cutting processes are chip-forming processes,

chip-control has been overlooked in manufacturing process control for a long time.

2

However, with the automation of manufacturing processes, machining chip-control

becomes an essential issue in machining operations in order to carry out the

manufacturing processes efficiently and smoothly, especially in today’s unmanned

machining systems.

After material is removed from the workpiece, it flows out in the form of chips.

After flowing out, the chip curls either naturally or through contact with obstacles. If the

material strain exceeds the material breaking strain, the chip will break. Chip flow, chip

curl, and chip-breaking are three main areas of chip-control research.

The most logical approach in developing cutting models for machining with

chip-breaking is to investigate and understand the absolute direction of chip flow, since

chip curling and the subsequent chip-breaking processes depend very heavily on the

nature of chip flow and its direction.

Chips have two flow types:

• Chip side flow - Chip flow on the tool face.

• Chip back flow - Chip flow viewed in a plane perpendicular to the cutting

edge. This type of flow indicates the amount of chip leaning toward the secondary face

(or the tool groove profile) of the tool in machining with grooved tools as well as tools

with complex tool face geometries.

The combined effects of these two chip flow types make a three-dimensional

chip flow, subsequently leading to three-dimensional chip curl and breaking.

For chip flow study, the most important objective is to establish the model of the

3

chip side-flow angle, which in most research is called the chip flow angle. Figure 1-1

shows chip side flow and chip back flow.

Chip side flow (Jawahir 1993) Chip back flow (Johnson, 1962)

Figure 1-1 Chip Flow

Naturally a chip will curl after it flows out. Contact with the chip-breaking

groove or chip breaker or other obstacles will also make a chip curl. There are three basic

forms of chip curl, and all shapes of free chips can be constructed by combinations of

these three basic shapes or straight chip:

• Chip up-curl

• Chip side-curl

• Chip lateral-curl. The chip lateral-curl was found in recent studies (Fang,

N. 2001).

The most important work for chip curl study is to establish models for the chip

up-curl radius and the chip side-curl radius, both of which have a very significant

influence on chip-breaking. Figure 1-2 shows chip up-curl and chip side-curl.

4

Chip side-curl Chip up-curl

Figure 1-2 Chip Side-curl and Chip Up-curl (Jawahir 1993)

Machining chips vary greatly in shape and length. In machining, short broken

chips are desired because unexpected long chips may damage the finished work-piece

surface; may break the inserts, or even hurt the operator. Therefore the study of

chip-breaking is very important for optimizing the machining process. Efficient

chip-control will contributes to higher reliability of the machining process, a

better-finished surface, and increased productivity.

Chip-breaking is a cyclic process. In each cycle a chip first flows out with some

initial curling. A chip will keep on flowing out until it comes into contact with and is

blocked by obstacles like the work-piece surface or the cutting tool. The chip curl radius

will then become smaller and smaller with the chip continuously flowing out. When the

chip curls tightly enough to make the chip deformation exceed the chip material breaking

strain, the old chip will break, and new chips will form, grow, and flow out.

5

The chip-breaking research problem includes many issues. Figure 1-3 shows the

main scope of chip-breaking study. The main goals of chip-breaking research is to

establish a chip-breaking prediction model for chip-breaking prediction, machining

process design, tool selection, and tool design.

Figure 1-3 Research Fields of Chip-Control

There are two main chip-breaking modes— chip-breaking by chip/work-surface

contact or chip-breaking by chip/tool flank-surface contact. In the first mode, a chip may

6

break by contact with the surface to be machined, which caused by chip side-curl; a chip

may, instead, break by contact with the machined surface, which is caused by chip

up-curl. The second breaking mode is three-dimensional chip-breaking caused by chip

side-curl.

There are three ways to break a chip:

• Change cutting conditions

• Change cutting a tool geometric features

• Design and use a chip breaker or chip-breaking groove

Increasing the depth of cut or the feed rate can significantly improve chip

breakability. However usually in industry this is not practical way due to the limitations

of the machining process. Therefore, optimizing the design of the cutting tool geometric

features and the chip breaker / chip-breaking groove is the most possible and efficient

way to break the chip.

Chip curl is limited in nature so that is difficult for breaking. In industry cutting

tools are usually grooved to help chip break. The chip-breaking groove can help a chip

curl more tightly to make the chip easier to break; and under particular conditions, the

chip-breaking groove can also reduce friction on a tool rake-face to reduce the power

consumption of the metal cutting process. The next section will discuss the chip-breaking

groove and the cutting tool classification.

7

1.2 Chip-Breaking Groove & Cutting Tool Classification

Corresponding to different applications, chip-breaking grooves vary greatly. To

investigate the chip-breaking groove’s effects on metal cutting, the chip-breaking groove

needs to be classified first. In this thesis, different chip-breaking models are developed

for cutting tools with different types of chip-breaking grooves, based on the

chip-breaking groove classification introduced in this section.

The cutting tool can be classified into five categories: flat rake face tools, tools

with block type chip breaker, tools with two-dimensional chip-breaking groove, tools

with three-dimensional chip-breaking groove, and tools with complicated geometry

modifications. Figure 1-4 illustrates the five kinds of cutting tools.

Commercial tools with complicated geometric modifications may include

pimples and dimples on the rake face, and waviness on the cutting edge. Such tools may

also contain combination of the above elements. In this thesis chip-breaking models are

developed for two-dimensional grooved cutting tools and for three-dimensional grooved

cutting tools.

8

(i) Straight Cutting Edge (ii) Chamfered Cutting Edge (iii) Rounded Cutting Edge (a) Flat Rake Face Tool (Jawahir, 1993)

(b) Tool with Block Type Chip Breaker

(c) Tool with Two-Dimensional Chip-Breaking Groove

(d) Tools with Three-Dimensional Chip-Breaking Groove

(e) Tools with Complicated Geometry Modifications

Figure 1-4 Classification of Chip Breaker / Chip-Breaking Groove

9

1.3 Chip-Breaking Limits

Chip-breaking limits are defined as the critical feed rate and the critical depth of

cut. When feed rate is larger than the critical feed rate, and depth of cut is larger than the

critical depth of cut, the chip will always break, otherwise the chip will not break. Figure

1-5 shows a chip-breaking chart.

Figure 1-5 A Sample Chip-Breaking Chart

Figure 1-6 illustrates a typical chip-breaking chart. Generally the chip-breaking

curve can be divided into three typical parts: up-curl dominated chip-breaking region AB,

side-curl dominated chip-breaking region CD, and transitional region BC.

Broken chips

Unbroken chips

The critical feed rate

The critical depth of cut

10

Figure 1-6 Typical Chip-Breaking Chart (Li, Z. 1990)

Up-curl Dominant Part AB and the Critical Feed Rate

In the part AB of the chip-breaking limit curve, shown above, the lowest point B

is the minimum feed rate. This part is primarily a straight line with a slope and can be

regarded as a two-dimensional chip-curling region. On each side of this part, the broken

area primarily consists of up-curled C-type chips, while the unbroken area primarily

consists of snarling chips. The objective of the theoretical analysis is to seek a formula

for estimating the minimum feed rate, which is defined as the Critical Feed Rate (fcr) (Li,

Z. 1990). In machining, cutting tools with line-arc grooves and line-arc-line grooves are

often used.

Side-curl dominant Part CD and the Critical Depth of Cut

The part CD of the chip-breaking limit curve involves side-curl dominated

11

chip-breaking processes. This part shows a complex three-dimensional chip curling (see

Figure 1-6). On each side of this part, the broken area is mainly composed of side-curled

spiral type continuous chips. Oblique-curl spiral continuous chips are also found in the

larger feed rate area. The minimum point in the horizontal coordinate corresponds to the

Critical Depth of Cut (dcr) (Li, Z. 1990). When the depth of cut is smaller than this

value, the chip usually does not break. The key is to seek the critical depth of cut. In this

case, side-curl ε type chips are usually generated.

Transitional Part BC

This part shows a more complex three-dimensional chip curling. On both sides of

this part are oblique curling spiral chips. When the number of chip rolls is few, the chips

are similar to C-type chips, otherwise they are ε or snarling-type chips.

The critical feed rate and the critical depth of cut are the two chip-breaking limits.

There is a chip-breaking condition: The chip will always break when the depth of cut is

greater than the critical depth of cut and the feed rate is greater than the critical feed

rate. Otherwise the chip will not break.

If the critical feed rate and the critical depth of cut could be predicted,

chip-breaking could then be predicted. This would greatly simplify chip-breaking

prediction research. The chip-breaking limits theory is the basis of the research

conducted in this dissertation.

12

2 The State of the Art This chapter reviews earlier efforts in chip-control research. For chip-control

research, two questions should be presented: How does a chip form and move in space?

And how does a chip break? In this chapter, previous investigations on chip flow, chip

curl, and chip-breaking are first reviewed, which are relevant to the first question. Next,

previous attempts to develop chip-breaking criteria are presented, which bear on the

second question. The Nakayama’s chip-breaking criterion, and Li’s work on

chip-breaking limits are reviewed in detail. This is particularly important because the

chip-breaking predictive models developed in this dissertation are based on chip-breaking

limits theory and Nakayama’s work. Finally, existing problems in chip-control research

are reviewed.

2.1 Chip Flow

Chip-breaking modes depend on the nature of chip flow and its direction.

Understanding the chip flow mechanism is important for chip-control. Chip flow is

determined by many factors and is usually described with the chip flow angle λψ . The

chip-flow angle is the angle between the chip-flow direction on the cutting tool rake-face

and the normal line of the cutting edge (see Figure 2-1). Establishing the model of the

chip flow angle is the main objective of chip flow research. Due to the extreme

13

complexity of the chip formation process, only limited success has been achieved in

chip-flow research, especially for three-dimensional conditions (three-dimensional

groove, and three-dimensional cutting).

Figure 2-1 Chip Flow Angle (Jawahir, 1993)

A lot of work has been done on chip-flow angle research during the last few

decades, and there are many methods for calculating the chip-flow angle.

The investigation of chip flow began with modeling over plane rake face tools.

Merchant, Shaffer and Lee used the plasticity theory to attempt to obtain a unique

relationship between the chip shear plane angle, the tool rake angle and the friction angle

between the chip and the tool (Merchant, 1945; Lee, 1951). Shaw (1953) proposed a

modification to the model presented by Lee and Shaffer. Palmer (1959) presented the

shear zone theory by allowing for variation in the flow stress for a work-hardening

material. van Turkovich (1967) investigated the significance of work material properties

and the cyclic nature of the chip-formation process in metal cutting. Slip-Line Field

λψ

14

Theory is widely applied in chip-formation research and some slip-line field models are

presented (Usui, 1963; Johnson, 1970; Fang, N. 2001). Being computationally successful,

Slip Line Field models do not agree well with experiment results due to lack of

knowledge of the high strain rate and temperature flow properties of the chip material.

Through studying the chip flow in free oblique cutting, Stabler presented a

famous “Stabler Rule” (Stabler, 1951):

skλψ λ = (2-1)

where the λψ is the chip flow angle, the λs is the cutting-tool inclination angle, and c is

a material constant. This rule is applicable for free oblique cutting.

Another chip-flow model is presented with the assumption that the chip flow is

perpendicular to the major axis of the projected area of cut. This model uses empirical

substitutions to consider the effect of cutting forces (Colwell, 1954). That is:

γγγ

ελ ψκκ

ψ −

⋅++= arctan

22tan1arctan dfr

d (2-2)

where d is the depth of cut, f is the feed rate, κγ is the cutting edge angle, rε is the nose

radius, and ψγ is the minor cutting edge angle. Since Colwell’s equation does not consider

the effect of the work-piece material, this model therefore will result in significant error

under particular conditions.

Okushima considered that chip flow is invariant with cutting speed and chip flow

should be the summation of elemental flow angles over the entire length of the cutting

edge (Okushima, 1959).

15

A chip flow model was presented by Young in 1987, assuming Stabler's flow rule,

with validity for infinitesimal chip width, and the directions of elemental friction forces

summed up to obtain the direction of chip flow (Young 1987).

The above chip-flow studies are all for chip side-flow angle λψ . Jawahir found

that a chip also has another form of flow — back flow and presented a chip back-flow

angle model (Jawahir 1988-a).

Chip flow is only a part of chip space movement. To understand the chip

movement mechanism, it is necessary to study chip curl.

2.2 Chip Curl

Chip curl has two basic modes: up-curl and side-curl. Recently the third chip curl

mode – lateral curl – was found (Fang, N. 2001). The different material flow speed in

different directions along the chip, results in different modes of chip curl. The chip

up-curl is much simpler than the other two kinds of chip curl; therefore the greatest

achievements have been in chip up-curl modeling. Chip side-curl is much more difficult

than up-curl and presently there are no applicable models of the chip side-curl. Study on

the lateral curl has only began recently.

2.2.1. Chip Up-Curl

Chip up-curl is the chip curl in the chip depth direction. The axis of chip up-curl

approximately parallels the chip / cutting tool rake-face detachment line. The up-curl

level is described with chip up-curl radius RC. In metal cutting, the material flow speed in

the chip bottom is generally greater than the material flow speed in the chip top surface,

16

which therefore results in chip up-curl. For the flat rake-face tool, Nakayama considered

that when there is a build-up edge on the cutting tool, the part of the chip that flows over

the build-up edge will come in contact with the tool rake-face, which brings a bent

moment to the chip (Nakayama, 1962-b). For the grooved tool, the chip-breaking groove

could help chip curl (see Figure 2-2).

Figure 2-2 Chip Up-Curl Process with Grooved Cutting Tool (Li, Z. 1990)

17

The chip up-curl radius has a critical influence on up-curl-dominated

chip-breaking. The main objective of chip up-curl research is to establish the model of

the chip up-curl radius.

It has been found that when chip flow angle ψλ is big enough, a chip will flow

through the whole chip-breaking groove (Jawahir, 1988-e). In this case the chip up-curl

radius is:

RC = R (2-3)

where R is the chip-breaking groove radius. When ψλ is small, a chip does not flow

through the whole chip-breaking groove. In this case, the chip up-curl radius is:

λψsin2BKR chC = (2-4)

where B is the chip-breaking groove width, Kch is a constant determined by the chip

material (Jawahir, 1988-e).

Based on chip/cutting tool geometric analysis, Li presented a chip up-curl radius

equation as:

+−= 2

2

cos21sin2 n

cn

n

c

n

nC W

lWlW

R γγ

(2-5)

Li’s work will be reviewed in detail later.

2.2.2. Chip Side-Curl

Chip side-curl is the chip curl in the direction of chip width. The side-curl axis is

generally perpendicular to the chip bottom surface. The chip side-curl can be described

with chip side-curl radius Ro. The chip side-curl is caused by differences in the material

18

flow speed along the chip width direction on the chip bottom surface (see Figure 2.3).

Figure 2-3 Mechanism of Chip Side-Curl

The chip side-curl radius has a critical influence on side-curl-dominated

chip-breaking. The main objective of chip side-curl research is to establish the model of

the chip side-curl radius.

Nakayama considered that the chip material had side flow, which leads to chip

side-curl. He also considered that the thicker the chip, the greater the chip material side

flow, therefore the greater the chip side-curl. He proposed following side-curl radius

equation, where bch is the chip width and hch is the chip thickness (Nakayama 1990):

chch hbR09.075.01

0

−= (2-6)

2.2.3. Chip Lateral-Curl and Combination Chip Curl

Study on the screwing curl has begun recently. In real cases, the chip curl form is

Chip

ρ

ω

V

Tool

Work-piece

19

a combination of the three basic curl forms: up-curl, side-curl, and lateral curl.

2.3 Chip-Breaking

As discussed in Chapter 1, chip-breaking has two basic modes: chip-breaking by

chip/work surface contact or chip-breaking by chip/tool flank surface contact. For

chip-breaking research, we need to set up the chip-breaking criteria; for industry

application, we need to find efficient ways to break chips.

The following is a summary of the two approaches of chip-breaking research:

1. Material stress analysis – to find the chip-breaking strain Bε .

Research work by this approach includes:

• Chip curl analysis (Nakayama, 1962; Z. Li, Z. 1990)

• FEA (Kiamecki, 1973; Lajczok, 1980; Strenkowski, 1985; etc.)

2. Experiment-based work

This approach uses the machining database to do chip-breaking prediction. Fang

and Jawahir have done a lot of work in establishing a database system based on fuzzy

mathematical model for chip breakability assessments (Fang, X. 1990-a, Jawahir, 1989).

This approach requires lots of time, money, and labor to establish the chip breaking

prediction database. With new work-piece materials, new cutting tools / lathe, and new

machining methods constantly coming out, it is difficult to establish and maintain a

chip-breaking database for chip-breaking prediction.

Tool designers optimize their tool design based on many cutting tests. In industry

machining process, some special devices such as rotating knife, a high-pressure gas/fluid

20

jet, and a vibrating cutting tool are also designed to break the chip. However, the most

efficient and most common way to break the chip is to use the chip-breaking groove /

chip breaker and optimize geometric features of the cutting tool.

Presently, there has been only limited success in the chip-breaking criterion

study. The theoretical achievements fall behind industry reality and requirements.

Equation (2-8) is the common chip-breaking criterion for up-curl-dominated

chip-breaking, presented by Nakayama (Nakayama, 1962-b). This work will be reviewed

in detail in Section 2.4.

−=>

)/1/1( LccB

RRhαεεε

(2-7)

where, ε is the chip maximum fracture strain, εB is the chip material breaking

strain, hc is the chip thickness, αhc is the distance from chip surface to its neutral layer, RC is

the chip flow radius, and RL is the chip-breaking radius

Presently most research on chip-breaking critera are for two-dimensional

chip-breaking. The chip-breaking criterion for three-dimensional chip-breaking needs

further investigation. three-dimensional chip-breaking criteria could not be established

without a reasonable two-dimensional chip-breaking model.

The finite element method has been applied in chip-breaking process analysis for

plane rake-face tools for orthogonal machining, and most recently for three-dimensional

machining (Kiamecki, 1973; Lajczok, 1980; Strenkowski, 1985, 1990). These analyses

are computationally successful, but their predictions do not agree with the experiments.

21

One reason could be the lack of knowledge of the high strain rate and temperature flow

properties of the chip material (Jawahir, 1993).

2.4 Nakayama's Chip-Breaking Criterion

Nakayama’s chip-breaking criterion (Equation 2-8) is the common chip-breaking

criterion in such research; therefore it is reviewed in detail here.

Nakayama considers that when the actual chip fracture strain (ε) is bigger than

the tensile strain on the chip (εB), the chip will break. It is noted that the ε is proportional

to the ratio of chip thickness and chip curl radius. That is:

C

ch

Rh

∝ε (Li, Z. 1990) (2-8)

where hch is the chip thickness, RC is the chip up-curl radius.

Nakayama considers that a chip flows out with up-curl radius RC, and then is

blocked by the work-piece surface or the cutting tool. With the chip material

continuously flowing out, the chip curl radius will be increasing continuously. When chip

reaches up-curl radius RL, whether it will break or not is determined by whether the chip

maximum fracture strain ε is greater than the chip material breaking strain εB.

Assuming chip cross-section shape is rectangle, we can calculate ε by the

following equation:

−=

LC

ch

RRh 112

ε (Li, Z. 1990) (2-9)

If the cross-section shape is not rectangular, the above equation can be written as:

22

−=

LCch RR

h 11αε (Li, Z. 1990) (2-10)

where α is cross-section shape coefficient; and αhch is the distance from neutral axis of

the chip cross section to the chip surface. Therefore we establish the chip-breaking

criterion:

BLC

ch RRh εα ≥

−

11 (Li, Z. 1990) (2-11)

2.5 Li’s Work on Chip-Breaking

Developing a reasonable chip-breaking criterion is the prerequisite for

establishing an applicable chip-breaking predictive model. However the extreme

complexity of the chip-breaking process makes the theoretical analysis and modeling of

chip-breaking very difficult. Based on Nakayama's work and chip-breaking limits theory,

through chip curl analysis, Li (1990) presented a new semi-empirical chip-breaking

model. Since it is the basis of the chip-breaking models developed in this research, it will

be reviewed in detail in the following part.

2.5.1. Theoretical Analysis of fcr and dcr

In the last chapter we reviewed the following chip-breaking condition based on

chip-breaking limits theory:

The chip will always break when the depth of cut is greater than the critical

depth of cut (dcr), and the feed rate is greater than the critical feed rate (fcr). Otherwise,

the chip will not break.

In Nakayama's model, for up-curl dominated chip-breaking region, the hch can be

23

calculated as:

hch C

fh γ

κsin= (2-12)

where γκ is the cutting edge angle, and Ch is the cutting ratio.

Substituting hc into Equation (2-8) we get:

−

=

hLc

cr

CRR

fγκα

εsin

)/1/1( (2-13)

When crff > , the chip will break. When crff ≤ , the chip will break.

crf is defined as the critical feed rate. From Figure 2-2 the crf equation for

up-curl dominated chips with two-dimensional grooved inserts can be obtained as

follows (Li, Z. 1990):

)cos21(sinsin2 nn

f

nr

RnhBcr W

lKWCf γγκα

ε−⋅⋅= (2-14)

where Wn is the width of chip-breaking groove, RK is the coefficient related to the chip

radius breaking:

KR=RL / (RL-RC) (2-15)

lc is the chip / tool contact length, κγ is the cutting edge angle, and γn is the rake angle in

normal direction.

As with fcr, a critical depth of cut (dcr) can be defined for the

side-curl-dominated chip-breaking region (Figure 2.4 and 2.5). The equation of dcr for

two-dimensional grooved inserts is as follows (Li, Z. 1990):

24

επ

αδρε rd Bcr )12

(cos −−= , for εrd ≥ (2-16)

εεα

δρεr

rd Bcr −= )

cos3.57(cos , for εrd < (2-17)

where ρ is the radius of side-curl chips, and δ is a chip cross section related parameter.

Figure 2-4 Chip Flow of Side-Curl Dominated ε-Type Chips (Li, Z. 1990)

25

Figure 2-5 A Segment of ε-Type Chip and Its Cross Section (Li, Z. 1990)

2.5.2. Semi-Empirical Chip-Breaking Predictive Model

The theoretical equations of dcr and fcr, shown above, cannot be used directly to

predict chip-breaking limits because not all parameters in the equation can be calculated

directly. Therefore a semi-empirical chip-breaking predictive model based on theoretical

equations of dcr and fcr is presented (Li, Z. 1990) for industry application.

The chip-breaking limits are influenced by a lot of factors but are mainly

determined by the work-piece material, cutting speed, and insert geometric features

(Figure 2-6).

Applying the single-factor modeling method, Li presented the following

chip-breaking predictive model:

dmdvdTcr

fmfvfTcr

KKKdd

KKKff

0

0

=

= (2-18)

26

Figure 2-6 Factors Influence Chip Breakability

where f0 and d0 is the standard critical feed rate and the standard critical depth of cut

under a predefined standard cutting condition. The predefined standard cutting condition

can be any cutting condition. KfT and KdT are the cutting tool (inserts) effect coefficient;

KfV and KdV are the cutting speed effect coefficient; and Kfm and Kdm are the work-piece

material effect coefficient. KdV and KfV are functions of cutting speed; Kdm and Kfm are

functions of workpiece material; and KdT and KfT are functions of cutting tool.

The empirical coefficients Kdm, KdV, KdT, Kfm, KfV, and KfT are developed through

cutting tests. Once the empirical equations of Kdm, KdV, KdT, Kfm, KfV, and KfT have been

set up, they can be calculated when the cutting condition is specified. Then the fcr and dcr

can be figured out under any conditions by multiplying the f0 and d0 with Kdm, KdV, KdT,

27

Kfm, KfV, and KfT, respectively. Therefore the chip-breaking can be predicted under any

given cutting condition.

Work-piece material coefficients Kdm and Kfm

Use Equation 2-21 to get the work-piece material constants. First, conduct a

group of cutting tests under predefined conditions with the given work-piece material,

then we can get a group of dcr and fcr; dividing them by the d0 and f0, we can then get the

coefficients Kdm and Kfm. Collecting all Kdm and Kfm for different work-piece materials,

we then can set up a work-piece material coefficients database.

0

0

/

/

ddK

ffK

crdm

crfm

=

= (

2-19)

When the predefined standard condition is changed, the above Kdm and Kfm

should multiply by a constant respectively. e.g. under condition 1, the chip breaking

limits got from cutting tests are f01 and d01, and under condition 2, the chip breaking

limits got from cutting tests are f02 and d02. Then when using condition 1 as predefined

standard cutting condition, we have 01/ ffK crfm = and 01/ ffK crfm = ; and when

using condition 2 as predefined standard cutting condition, we have 02/ ffK crfm =′ and

02/ ffK crfm =′

Cutting speed coefficients KdV and KfV

Use Equation 2-22 to set up the cutting speed empirical equations. First, conduct

several groups of cutting tests under predefined conditions, except changing the cutting

speed for several levels. Then we can get several groups of dcr and fcr; dividing them by

28

the d0 and f0, we can then get several KdV and KfV. Then we can use curve-fit to develop

the general empirical equations for the KdV and KfV. After the empirical equations are

established we can figure out KdV and KfV for any cutting speed without conducting any

extra cutting tests.

ddcrdV

ffcrfV

bVaddK

bVaffK

+==

+==

0

0

/

/ (2-20)

If the predefined standard condition is different, the above equations of the KdV

and KfV should multiply by a constant respectively.

Insert geometric coefficients KdT and KfT

Li (1990) set up the KdT and KfT models for two-dimensional grooved inserts as

follows. The predefined standard condition is still the same as before. The KdT and KfT are

developed as functions of the insert nose radius εr , the chip-breaking groove width Wn

and the cutting edge angle rk .

fWnfkfrfT KKKK r ××= ε (2-21)

where εfrK is the nose radius effect coefficient, rfkK is the cutting edge angle effect

coefficient, and fWnK is the width of the chip-breaking groove effect coefficient.

dWndkdrdT KKKK r ××= ε (2-22)

where εdrK is the nose radius effect coefficient, rdkK is the cutting edge angle effect

coefficient, and dWnK is the width of the chip-breaking groove effect coefficient.

In this research, an improved model based on Li’s model will be developed along

with the experimental study, which will be described in Chapter 4.

29

2.6 Existing Problems

For today’s unmanned manufacturing systems, chip-control needs to be

considered as important as tool wear, cutting forces, surface finish, and machining

accuracy. It is essential to develop an efficient chip-breaking prediction tool to optimize

the machining processes. Presently, a big gap still exists between analytical work and

practical requirements in the chip-control field. Three main problems exist in the

chip-breaking prediction research:

1. The chip-breaking prediction model for two-dimensional grooved inserts is not

complete.

Li’s semi-empirical model provides a solid base for chip-breaking prediction for

two-dimensional grooved inserts. However some important insert geometric features (e.g.,

the rake angle), which have significant influence on chip-breaking, are not included in

the model.

2. Lack of chip-breaking prediction model for three-dimensional grooved inserts.

Three-dimensional grooved inserts are the most popular inserts in finish cutting

in industry. It is crucial for chip-control to establish an efficient chip-breaking prediction

model for three-dimensional grooved inserts.

3. Current industry solutions are very costly.

Currently research in the practical application of chip-control is a very

time-money-labor-consuming job. An easy-to-maintain chip-breaking prediction system,

which does not require a huge number of cutting tests, is required by the machining

30

industry. For online chip-control, the system should be accessible through the Internet.

31

3 Objectives and Scope of Work 3.1 Approach

To optimize the machining process, chip-control is very important. Developing

an efficient chip-breaking predictive tool is essential to the machining industry. The tool

should fulfill the following industry requirements:

1. Predict whether a chip breaks under given cutting conditions when the

cutting tool is specified.

2. Optimize cutting-tool design and cutting condition design to make chip

break.

Presently, there is a big gap between the theoretical research and the above stated

industry requirements. Most industry cutting processes employ oblique cutting with

three-dimensional grooved cutting tools, while most successful analytical models are for

orthogonal cutting with simple grooved tools. For oblique cutting with three-dimensional

grooved cutting tools, there is a lack of fully reasonable chip-breaking criterion.

Therefore presently database-based systems are used for chip-breaking prediction and a

"try and see" method is used for tool design / selection in industry applications. Both

methods are very costly.

The semi-empirical chip-breaking model approach (Li, Z. 1990), shown in the

32

Chapter 1, is a practical way to bridge the gap, with great advantages:

1. It concentrates on the chip curl process instead of the chip formation process

so that it avoids the extremely complicated chip flow issue.

2. Supported by the chip-breaking limits theory, it only needs to consider the

up-curl dominated chip-breaking process and the side-curl dominated chip-breaking

process for chip-breaking prediction. Therefore the problem is greatly simplified.

3. It does not fully rely on theoretical analysis. Instead, it uses limited cutting

tests to develop the semi-empirical equations of chip-breaking limits. The number of

cutting tests needed to develop the semi-empirical models is greatly reduced in

comparison with present industry chip-breaking databases.

4. The semi-empirical chip-breaking model is intended for oblique cutting with

grooved cutting tools, so that is an appealing solution for industry application.

Given these advantages, the semi-empirical model approach is applied in this

research.

3.2 Objectives

The objective of this research is to develop a semi-empirical chip-breaking

predictive system for oblique steel turning with grooved cutting tools. It contains three

parts:

1. Extending Li’s semi-empirical chip-breaking predictive model for

two-dimensional grooved inserts to include important geometric features of cutting tools.

33

The effects of the cutting tool's rake angle, land length, land rake angle, and

backwall height, which are important for chip-breaking but are not considered in Li’s

model, are studied and included in the expanding model.

2. Developing a semi-empirical chip-breaking predictive model for

three-dimensional grooved inserts.

The chip-breaking problems mainly exist in the finish cutting, where the depth of

cut is small. More than 70% of the industry inserts used in finish cutting are

three-dimensional grooved inserts. The particular significance of this work is that it

presents an applicable predictive tool for three-dimensional grooved inserts.

3. Developing a web-based semi-empirical chip-breaking predictive system.

For online chip-breaking prediction and tool /cutting condition design in industry

applications, it is important to develop a web-based chip-breaking predictive system

based on a reasonable chip-breaking predictive model.

3.3 Outline of the Dissertation

This section provides an overview of how the rest of the dissertation is

organized.

Chapter 4 is the extended study on chip-breaking limits for two-dimensional grooved

inserts. Through chip / insert geometric analysis, the original model of the chip-breaking

limits are extended to include the insert rake angle, land length, land rake angle and

backwall height effects. New equations of the critical feed rate and the critical depth of

cut are presented in this chapter. Li’s semi-empirical chip-breaking model is then

34

extended to include those features. Experiments are conducted to develop the empirical

equations for the modification coefficients of the insert geometric features.

Chapter 5 presents the semi-empirical chip-breaking predictive models for

three-dimensional grooved inserts. The definition of the three-dimensional grooved

inserts is given first. The chip-breaking limits are then described as functions of the insert

geometric feature parameters. The semi-empirical chip-breaking model for

three-dimensional grooved inserts are then established. Cutting tests are conducted to

develop the semi-empirical equations. The experiment-based approach is also used for

developing an experimental based chip-breaking prediction model.

Chapter 6 presents a web-based chip-breaking predictive system. The system is a

powerful chip-control tool that is accessible through the Internet. This chapter introduces

the system structure and the system user interface.

Chapter 7 summarizes all work in this dissertation and describes the possible future

directions in developing chip-breaking predictive models.

35

4 Extended Study on Chip-Breaking Limits for Two-Dimensional Grooved Inserts

This chapter discusses chip-breaking for two-dimensional grooved inserts. The

definition of the two-dimensional grooved insert is given first. Then an improved

semi-empirical model of the chip-breaking limits is developed in this part.

4.1 Geometry of Two-Dimensional Grooved Inserts

The cutting tool classification has been defined in Chapter 1. For

two-dimensional grooved inserts, the groove width along the cutting edge is the same,

except the two ends of the groove. Figure 4.1-1 shows the geometry of two-dimensional

grooved inserts.

b

W

o1o

h

1

Figure 4-1 Geometry of Two-Dimensional Grooved Inserts

A A

A-A

36

4.2 The Critical Feed Rate (fcr)

In this section, theoretical analysis is conducted to get the improved equation of

the critical feed rate, which contains four more geometric parameters than Li’s equation

of the critical feed rate (see Equation (2-15)).

The equation of the fcr developed by Li is:

cr

rhbcr R

kcfκ

εsin2

= (4-1)

To get the theoretical equation of fcr, the equation of the chip up-curl radius cR

should be calculated first.

4.2.1. Equation of the Chip Up-curl Radius RC

Figure 4-2 shows the geometric parameters of the insert, where lc is the chip-tool

rake-face contact length, h is the backwall height, γ0 is the rake angle, and W is the

chip-breaking groove width, measured along the tool rake face. Then the Rc can be

presented as:

)cossin(2)sincos(2

)cossin(2)cossin(])sincos[(

00

00222

00

200

200

γγγγ

γγγγγγ

hWhWllhW

hWhWlhW

R

cc

cc

++−+++

=

+++−−

=

(4-2)

37

Figure 4-2 The Geometric Parameters of Two-Dimensional Grooved Insert (1)

As shown in Figure 4-2, because 1WWWn += (4-3)

And cf lll += (4-4)

Just as in Li’s work, the parameter lf can be calculated as:

nf Wl β ′= (4-5)

where β’ is a coefficient estimated experimentally to be equal to 0.2 for carbon steel

machining (Li, Z. 1990).

As shown in Figure 4-3, by substituting Equation (4-5) into Equation (4-4), the lc

becomes:

chip

W1

Wn

γ0

lc

W

h

O

lf

Rc Work-piece

tool

38

)1cos()cos()cos(

00

011 −+

−+′= γβ

αγαγ

β rc bWl (4-6)

Figure 4-3 The Geometric Parameters of Two-Dimensional Grooved Insert (2)

Then the Rc can be calculated as:

)cossin(2)cos()cos(

)sincos()cos()cos(

2

)cossin(2

))cos()cos(

sincos(2

00

20

2012

1000

011

00

0

01100

222

γγαγαγ

γγαγαγ

γγαγαγ

γγ

hW

bhWb

hW

bhWllhWR

rr

rff

c

++−

+−+−

++

+−

+−−++=

(4-7)

lf

γ0

α γ0

W1

Wn

l

W

lc

br1

α

39

4.2.2. Equation of the Critical Feed Rate fcr

By substituting Equation (4-7) to Equation (4-1), the new theoretical model of fcr

can be established as:

++−

+−+−

++

+−

+−−++

⋅=

)cossin(2)cos()cos(

)sincos()cos()cos(

2

)cossin(2

))cos()cos(

sincos(2

sin2

00

20

2012

1000

011

00

0

01100

222

γγαγαγ

γγαγαγ

γγαγαγ

γγ

κε

hW

bhWb

hW

bhWllhW

kcf

rr

rff

r

rhbcr (4-8)

The above equation shows fcr is the equation of the insert geometric parameters,

cutting speed and work-piece material. It can be used to analyze the effect of the insert

geometric parameter on chip-breaking.

4.3 The Critical Depth of Cut

The critical depth of cut determines the chip-breaking range in the

side-curl-dominated chip-breaking region. Applying Nakayama’s chip-breaking criterion:

−=

LchB RR

h 11

0

αε (4-9)

where chhα is equal to the distance from neutral axial plane of the chip to the chip

surface (Li, Z. 1990). It can be calculated as (Li, Z. 1990) Equation 4-10.

3cb

h chch+

=α (4-10)

where bch is the chip width.

40

01 →LR

Q

0Rhch

Bα

ε =∴ (4-11)

Applying the chip side-curl radius equation 4-11 (Li, Z. 1990):

kabR109.075.01

210

−=

ξξ (4-12)

where the 1ξ is the chip-width distortion coefficient and 2ξ is the chip thickness

distortion coefficient. That is,

atbb chch 21 ξξ == (4-13)

where k is a modification coefficient to the chip side-curl radius. tch is the chip thickness.

a, b, and c are chip cross-section geometric parameters and are shown in Figure 4-4.

Substituting Equation 4-12 to 4-11, Bε can be calculated as:

kabcb

B109.075.0

3 211

−

+=

ξξξ

ε (4-14)

Calculating Equation (4-14) as an equation of variable b, we have,

( )qppb 12.006.01 2

1

+±−=ξ

(4-15)

where

( )

=+−=

acqcakp B

2

2

25.003.025.0

ξξε

(4-16)

41

Figure 4-4 A Segment of a ε-Type Chip and Its Cross Section (Li, Z. 1990)

From Figure 4-5, a and b can be calculated as a function of the chip flow angle

λψ , (Li, Z. 1990)

( )λκ Ψ−= rfc cos (4-17)

When ( ) εε κ rfrd r 2,cos1 ≤−≤

( ) ( )

+

−=

=−+−=

εε

ελ

λε

λλε

ψ

ψψκψ

rf

rdr

rbfra

cr

r

2arcsinarccos

21

sin2sincos1

(4-18)

When ( ) εε κ rfrd r 2,cos1 ≤−≥

( ) ( )

( )

( )

++−=

−−=∠=

Ψ−

−+−=

Ψ−+

Ψ−−=

cr

r

crrr

r

r

r

r

df

dr

rdr

BAO

rdfrb

fra

22tancotarccot

cos1sin

arctan

sin4

sinsin

sin1

22

κκκψ

κκ

β

κ

κβ

β

ελ

ε

ε

λ

εε

λλ

ε

(4-19)

a

42

Figure 4-5 Depth of Cut and Cutting Flow Angle (Li, Z. 1990)

Substituting a, b and c to Equation 4-14, the dcr can be got as,


−

++−−=

εεεε ξ r

fr

qpprrdcr 2

arcsin12.0

12.0arcsin2cos

1

2

(4-20)


( ) ( )λεε κξ Ψ−++−+−−= rcr qppfrrd sin12.0

06.01

42

1

22 (4-21)

Equation (4-8) cannot be used to calculate fcr directly, since a few variables in the

equation cannot be predicted, for example, the cutting ratio Ch and the lf. Also both sides

of the Equation 4-20 and 4-21 contains dcr so that they can not be used to calculate dcr

directly too. To apply the theoretical model in industry, a semi-empirical model has to be

developed; this is illustrated by Equation (2-19). Cutting tests have been conducted to

develop the model.

43

4.4 Semi-Empirical Chip-Breaking Model

for Two-Dimensional-Grooved Inserts

Recalling the semi-empirical model of fcr and dcr:

dmdvdTcr

fmfvfTcr

KKKdd

KKKff

0

0

==

where

dWndkdrdT

fWnfkfrfT

KKKK

KKKK

r

r

⋅⋅=

⋅⋅=

ε

ε

To take the rake angle, back-wall height, land length, and land rake angle’s

effects into account, the equation of KfT and KdT are modified as follows:

1010

1010

γε

γε

γγ

γγ

dbdhddndWdrdT

fbfhffnfWfrfT

KKKKKKK

KKKKKKK

⋅⋅⋅⋅⋅=

⋅⋅⋅⋅⋅= (4-22)

The modification coefficients 0γf

K , 1rfb

K , 01γf

K , fhK , 0γdK , 1rdbK , 01γdK ,

and dhK have been added to the model. The semi-empirical chip-breaking model for

two-dimensional grooved inserts are then extended to the following form:

44

(4-23)

The original modification coefficients rfK κ , nfwK , εfrK , rdK κ , ndwK , and

εdrK have been developed as linear functions of the relative parameters (Li, Z. 1990).

The unknown coefficients 0γf

K , 1rfb

K , 01γf

K , fhK , 0γdK , 1rdbK , 01γdK , and dhK

will be developed in the same way. For example, the 0γf

K will be in the form of:

baK f += 00 γγ

where a and b are constants that will be got from experimental study.

Therefore the purpose of the experiments is to get the coefficients 0γf

K , 1rfb

K ,

01γfK , fhK , 0γdK , 1rdbK , 01γdK , and dhK .

4.5 Experimental Work

This chapter introduces the experimental study done for the extended model of

the chip-breaking limits.

fmfvfTcr KKKff 0=

1010 γε γγ fbfhffnfWfrfTKKKKKKK ×××××=

)(VFK ffV =

)(mFK ffm =

1010 γε γγ dbdhddndWdrdTKKKKKKK ×××××=

dmdvdTcr KKKdd 0=

)(VFK ddV =

)(mFK ddm =

45

4.5.1. Design of the Experiments

To get the coefficients 0γf

K , 1rfb

K , 01γf

K , fhK , 0γdK , 1rdbK , 01γdK , and

dhK , eighteen inserts were designed to be used in the experiments. Their designed

geometric parameters are listed in Table 4-1. All inserts used here has a 1mm nose radius

Table 4-1 Insert Geometric Parameters Design Insert

Number γ0 bγ1 γ01 h Other

Parameters 1 10 ˚ 0.2 mm -10 ˚ 0 mm 2 14 ˚ 0.2 mm -10 ˚ 0 mm 3 18 ˚ 0.2 mm -10 ˚ 0 mm 4 22 ˚ 0.2 mm -10 ˚ 0 mm 5 18 ˚ 0.05mm -10 ˚ 0 mm 6 18˚ 0.1 mm -10 ˚ 0 mm 7 18 ˚ 0.2 mm -10 ˚ 0 mm 8 18 ˚ 0.3 mm -10 ˚ 0 mm 9 18 ˚ 0.4 mm -10 ˚ 0 mm 10 18 ˚ 0.2 mm 0 ˚ 0 mm 11 18 ˚ 0.2 mm -5 ˚ 0 mm 12 18˚ 0.2 mm -10 ˚ 0 mm 13 18˚ 0.2 mm -15 ˚ 0 mm 14 18 ˚ 0.2 mm -20 ˚ 0 mm

κγ= 90˚ λs= -6˚ α0= 6˚ κγ'= 30 ˚

15 18 ˚ 0.2 mm -10 ˚ 0 mm 16 18 ˚ 0.2 mm -10 ˚ 0.1 mm 17 18 ˚ 0.2 mm -10 ˚ 0.2 mm 18 18 ˚ 0.2 mm -10 ˚ 0.4 mm

κγ= 90˚ λs= -6˚ α0= 6˚ κγ'= 30 ˚

Note: the shaded parameters are predefined standard inserts

The predefined standard cutting condition is listed below:

Work-piece material: 1045 steel;

Surface feeding speed: Vc= 100 m/min;

Nose radius: 1mm

Main cutting-edge angle: 90˚

46

4.5.2. Experimental Results

The chip-breaking limits obtained from the cutting tests are listed in Table 4-2.

Table 4-2 Cutting Test Results

No. 0γ

(Deg)

01γ

(Deg)

1γb

(mm)

h (mm)

fcr (mm/rev)

dcr (mm)

1 10 -10 0.2 0 0.2 0.8 2 14 -10 0.2 0 0.18 0.8 3 18 -10 0.2 0 0.18 0.8 4 22 -10 0.2 0 0.15 0.8 5 18 -10 0.05 0 0.1 1 6 18 -10 0.1 0 0.15 1 7 18 -10 0.2 0 0.18 0.8 8 18 -10 0.3 0 0.18 1 9 18 -10 0.4 0 0.2 1 10 18 0 0.2 0 0.2 1 11 18 -5 0.2 0 0.2 1 12 18 -10 0.2 0 0.18 0.8 13 18 -15 0.2 0 0.2 1 14 18 -20 0.2 0 0.2 1 15 18 -10 0.2 0 0.18 0.8 16 18 -10 0.2 0.1 0.15 0.8 17 18 -10 0.2 0.2 0.1 0.8 18 18 -10 0.2 0.4 0.05 0.8

To make the experimental results as reliable as possible, all the tests are repeated

three times under the same experimental conditions at different times. Furthermore,

cutting tests around the breaking / non-breaking boundary of the chip-sample charts are

repeated more times to make the values of fcr and dcr as accurate as possible. Part of the

sample chip-breaking charts are listed in Appendix I.

47

4.5.3. Experimental Data Analysis

The following empirical equations of the modification coefficients had been

developed from the experimental results:

00 0208.032.1 γγ −=fK (4-24)

10 =γdK (4-25)

152.1696.01 γγ bK fb += (4-26)

11

=γdb

K (4-27)

101 =γfK (4-28)

101 =γdK (4-29)

hK fh 84.11 −= (4-30)

1=dhK (4-31)

The predefined standard values are:

• Rake angle: 12°.

• Land Length: 0.2mm

• Land Rake Angle: -10°

• Raised backwall height: 0mm

Next the experimental results of the rake angle, back-wall height, land length,

and land rake angle will be analyzed one by one through comparison with the calculation

results of the theoretical equations developed in this chapter. Equation (4-8) is used to

calculate theoretical predicting values of fcr .

Both previous work (Li, Z. 1990) and our cutting tests show that for

two-dimensional grooved inserts the critical depth of cut is mainly determined by the

48

insert nose radius. Other insert geometric features only have minor effects on the critical

depth of cut. That is to say:

εrdcr ≈ (for two-dimensional grooved inserts) (4-32)

Equation (4-32) is used to calculate theoretical predicting values of dcr.

4.5.3.1. Rake Angle

For grooved inserts, a larger rake angle means a larger groove depth Wn, which

could make the chip-curl tighter, so that the chip breakability improves. It is found that

the experimental values of the fcr slightly decrease with the increase of the rake angle,

which matches the theoretical models well.

Equation (4-8) does not take effects of friction on the rake face into account,

which may explains the difference between the theoretical fcr and the experimental results.

The friction can increase chip deformation to improve chip breakability, thus the test

results of fcr will be smaller than the theoretical values of fcr.

For dcr, the rake angle only has slight influence. Therefore when changing the

rake angle, the dcr remains the same value (0.8mm), which is close to the insert nose

radius (1.0mm).

Figure 4-6 shows the comparison of the theoretical values, empirical equation

predicting values, and the experimental results when changing the insert rake angle.

4.5.3.2. Land Length

When the land length increases, the actual chip/rake face contact length and the

groove width will increase, too, so that the chip up-curl radius will increase, leading to a

49

larger fcr . It should have minor influence on dcr .

The calculation results show that the fcr increases with the increase in the land

length. The dcr keeps close to the insert nose radius.


predicting values, and the experimental results when changing the insert land length.

4.5.3.3. Land Rake Angle

In general, the land rake angle should have little influence on chip-breaking

when it is not very great due to the effects of the chip-flow sticking region.

The calculation results clearly show that the land rake angle has very little

influence on chip breakability. The critical feed rate and the critical depth of cut almost

do not change with the change of the land rake angle.


predicting values, and the experimental results when changing the insert land rake angle.

4.5.3.4. Raised Backwall Height

The increase of the back-wall height will force the chip to up-curl more tightly,

which will improve the chip breakability. The calculation results clearly show that the

critical feed rate will decrease with the increase of the back-wall height, which matches

the theoretical prediction well. The critical depth of cut is still determined by the nose

radius. The raised backwall height only has insignificant influence on dcr.


predicting values, and the experimental results when changing the insert backwall height.

50

0

0.1

0.2

0.3

0.4

0.5

0.6

10 12 14 16 18 20 22

Rake Angle (deg.)

fcr (

mm

/rev)

Theoretical ResultExperimental ResultEmpirical Model Result

Theoretical / experimental / empirical model results of fcr

00.20.40.60.8

11.21.41.61.8

2

10 12 14 16 18 20 22Rake Angle (deg)

dcr (

mm

)

Theoretical ResultEmpirical Model ResultExperimental Result

Theoretical / experimental / empirical model results of dcr

Figure 4-6 Rake Angle and Chip-Breaking Limits

51

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Land Length (mm)

fcr (

mm

/rev)

Theoretical Result

Experimental Result

Empirical Model Result


00.20.40.60.8

11.21.41.61.8

2

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Land Length (mm)

dcr (

mm

)



Figure 4-7 Land Length and Chip-Breaking Limits

52

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

-20 -15 -10 -5 0Land Rake Angle (deg.)

fcr (

mm

/rev)



00.20.40.60.8

11.21.41.61.8

2

-20 -15 -10 -5 0

Land Rake Angle (deg)

dcr (

mm

)



Figure 4-8 Land Rake Angle and Chip-Breaking Limits

53

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

0 0.1 0.2 0.3 0.4

Backwall height (mm)

fcr (

mm

/rev)



0

0.20.4

0.60.8

1

1.21.4

1.61.8

2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Backwall Height (mm)

dcr (

mm

)



Figure 4-9 Raised Backwall Height and Chip-Breaking Limits

54

4.6 Summary

In this chapter, the chip-breaking prediction for two-dimensional grooved inserts

has been studied. The insert geometric parameters — the rake angle, the land length, the

land rake angle, and the raised backwall height — are taken into consideration when

developing the chip-breaking prediction model. Work done in this section includes three

parts:

1. The theoretical equations of the chip-breaking limits are developed as:

++−

+−+−

++

+−

+−−++

⋅=

)cossin(2)cos()cos(

)sincos()cos()cos(

)cossin(2

))cos()cos(

sincos(2

sin2

00

20

2012

1000

011

00

0

01100

222

γγαγαγ

γγαγαγ

γγαγαγ

γγ

κε

hW

bhWb

hW

bhWllhW

kcf

rr

rff

r

rhbcr

and


−

++−−=

εεεε ξ r

fr

qpprrdcr 2

arcsin12.0

12.0arcsin2cos

1

2


( ) ( )λεε κξ Ψ−++−+−−= rcr qppfrrd sin12.0

06.01

42

1

22

2. An extended semi-empirical chip-breaking prediction model is developed as:

55

3. The modification coefficients for the rake angle, the land length, the land rake

angle, and the raised backwall height have been developed through experiments:

00 0208.032.1 γγ −=fK 10 =γdK

152.1696.01 γγ bK fb += 11 =γdbK

101 =γfK 101 =γdK

hK fh 84.11 −= 1=dhK

fmfvfTcr KKKff 0=

1010 γε γγ fbfhffnfWfrfTKKKKKKK ×××××=

)(VFK ffV =

)(mFK ffm =

1010 γε γγ dbdhddndWdrdTKKKKKKK ×××××=

dmdvdTcr KKKdd 0=

)(VFK ddV =

)(mFK ddm =

56

5 Chip-Breaking Predictive Model for Three-Dimensional Grooved Inserts

This chapter discusses chip-breaking for three-dimensional grooved inserts,

which are the most popular type of inserts for medium / finish steel turning in industry.

The definition of the three-dimensional grooved inserts will be given first. A few key

geometric parameters are used to define the geometric features of three-dimensional

grooved inserts. Their influence on chip-breaking will be analyzed. Cutting experiments

ar

machining chip-breaking prediction with grooved inserts in ......grooved cutting tools, and a...

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